An algorithm for a general minimum fuel control problem

In the paper we describe an algorithm for a general minimum fuel control problem. The objective function of the problem is represented by the functional: F⁰(x(·), u(·))=F^0,1(x(·), u(·))+F^0.2(x(·),u(·)) where F^0,1 is continuously differentiable with respect to state x(·) and control u(·), while F^0,2 includes terms ∫₀(t_j) Σ_i=1^mg_i(x(t),t)|u_i (t)-u_u^r(t)|dt. A direction of descent of the algorithm is found by minimizing certain Hamiltonian. An efficient version of a proximity algorithm is used to solve this subproblem. State and terminal constraints are treated via an exact penalty function. The algorithm is globally convergent in the sense that every accumulation point of a sequence generated by the algorithm satisfies the maximum principle condition